Some Group Theoretical Aspects of Nonlinear Quantal Oscillators

DOI

10.2991/jnmp.2005.12.s1.3How to use a DOI?

Abstract

We investigate the algebraic properties of the time-dependent Schrödinger equations of certain nonlinear oscillators introduced by Calogero and Graffi (Calogero F & Graffi S, On the quantisation of a nonlinear Hamiltonian oscillator Physics Letters A 313 (2003) 356-362; Calogero F, On the quantisation of two other nonlinear harmonic oscillators Physics Letters A 319 (2003) 240-245; Calogero F, On the quantisation of yet another two nonlinear harmonic oscillators Journal of Nonlinear Mathematical Physics 11 (2004) 1-6). Although all of the corresponding classical Hamiltonians are characterised by the Lie algebra sl(2, R), we find that the algebras in the quantal case are not unique and depend upon the choice of parameters made in the quantisation process.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - K. Andriopoulos
AU  - P.G.L. Leach
PY  - 2005
DA  - 2005/01/01
TI  - Some Group Theoretical Aspects of Nonlinear Quantal Oscillators
JO  - Journal of Nonlinear Mathematical Physics
SP  - 32
EP  - 42
VL  - 12
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s1.3
DO  - 10.2991/jnmp.2005.12.s1.3
ID  - Andriopoulos2005
ER  -